Inferring the information structure of scientific documents is useful for many NLP applications. Existing approaches to this task require substantial human effort. We propose a framework for constraint learning that reduces human involvement considerably. Our model uses topic models to identify latent topics and their key linguistic features in input documents, induces constraints from this information and maps sentences to their dominant information structure categories through a constrained unsupervised model. When the induced constraints are combined with a fully unsupervised model, the resulting model challenges existing lightly supervised feature-based models as well as unsupervised models that use manually constructed declarative knowledge. Our results demonstrate that useful declarative knowledge can be learned from data with very limited human involvement.